# Code for Transfer Operator and Dynamic Laplacian Computations

#### Contents

- Automatic almost-invariant set / coherent set extraction from Sparse Eigenbasis Approximation (SEBA)
- Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories
- Summary of transfer operator methods circa 2013

### 1. Automatic almost-invariant set / coherent set extraction from Sparse Eigenbasis Approximation (SEBA)

When searching for several to many almost-invariant sets or coherent sets, these sets sometimes need to be disentangled from several eigenvectors. The paper and code below perform this separation automatically by representing the eigenspace spanned by the eigenvectors in a basis whose vectors are sparse. Each of the vectors in this basis is supported on a single almost-invariant or coherent set.

### 2. Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories

Mesh-based method of computing finite-time coherent sets, particularly suited for sparse, scattered trajectories such as those obtained by physical observations (e.g. drifters, floats, etc...)

### 3. Summary of transfer operator methods circa 2013

Below are slides and code for a tutorial on transfer operator methods, presented at a Banff Workshop in 2013

- Slides for a short tutorial on transfer operator calculations in Matlab.
The slides cover:
- Computation of a transition matrix
- Propagation of a probability measure
- Computation of almost-invariant sets
- Computation of coherent sets
- Computation of the finite-time entropy (FTE) field
- Computation of absorption/hitting times
- Computation of topological entropy

#### Matlab code, data, images, from the tutorial

- Matlab code to perform the computations.

The three mat-files with "script" in the filename are
are the three main demos.

For the purposes of the time-constrained real-time tutorial, the code has been set up to run quickly; from a fraction of a second to two minutes.

Please see the readme file for more details.
- Matlab data files to run the Matlab code.
- Image files that are created by the Matlab code.

Higher resolution images can be obtained by altering the resolution (GAIO subdivision depth) in the matlab code.
- My relevant journal publications.